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# In parallelogram DEFG, the difference between two adjacent angles is 32 degrees. Which is the measure of the larger angle?

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In parallelogram DEFG, the difference between two adjacent angles is 32 degrees. Which is the measure of the larger angle?

A. 96 degrees

B. 114 degrees

C. 106 degrees

D. 118 degrees

In a regular pentagon ABCDE and regular hexagon MNOPQR, 2AB = 3MN and CD + QR = 10. Which is 4BC + 5PQ?

A. 44

B. 33

C. 42

D. 38

Jan 15, 2020

#1
+109739
+3

First one

In a parallelogram, two adjacent angles  sum to 180°

So

x  + (x - 32)  =  180

2x - 32  =  180         add 32 to both sides

2x  =   212                divide both sides by  2

x  = 106°

Jan 15, 2020
#2
+109739
+3

Let the  side of the pentagon  = x  and the side of the hexagon  =  y

2AB  = 3MN

CD  + QR    = 10   ......so.....

2x  = 3y

x  +  y  =  10

2x  - 3y    =  0

x    +  y  =  10              multtiply  the second equation by 3

2x  -  3y  =  0

3x   + 3y   = 30          add these

5x  =  30

x  = 6

And y  = 4

So

4BC + 5PQ  =

4(6) + 5(4)  =

24  +  20  =

44

Jan 15, 2020